Dating game

Earlier today I asked you the following puzzle: In front of you are three doors. Behind each door is a prospective partner. Your mission is to couple up with your best possible match. Imagine you chose a door at random. If you couple up with the person behind it, the chance you get your best match is 1 in 3. You can assume that of the three people who are waiting behind the doors, there is a best match, a not so good match, and a least good match for you.

But there are rules: To start, you select a door. It will open to reveal one of your potential suitors. If you want to choose this person as your match, you can.

You couple up with them. If you decide to move on, you discard the first person. You select one of the two remaining doors. It opens to reveal someone else. Again, you can choose this person as your match.

Nor are you allowed to return to the person you discarded behind the first door. If you decide to move on a second time, you select the final door. You must choose the person behind it as your match, whatever you think of them. If you want to see them all, you must choose the last. What strategy gives you the best chance of finding your best match?

Can you improve your odds from 1 in 3? You must assume that you know nothing about the average attractiveness of the group that the suitors are selected from.

If you see the most attractive person you have ever seen behind the first door, there is still a 50 per cent chance that the person behind the second door is even more attractive. The question is not psychological or sociological: The puzzle is mathematical: Solution The most concise answer was suggested by reader Michael John: You must use the first person as a reference for what comes next. In more detail, and with some maths, the strategy is this: Select a door, and reject the person behind it.

Select a second door, and proceed as follows. If you think that this person is a better match than the person behind the first door, choose them. If you think that this person is a worse match than the person behind the first door, reject them. Your choice is the person behind the final door. There are three possible cases for the person behind the first door: The strategy tells us to reject A.

Since A is the best match, in this case you wont get your best match. The strategy tells us to reject B, and choose another door: If we get C, we reject them, since C is a worse match than B. We end up with A, our best match. If we get A, we choose them, since A is a better match than B. The strategy tells us to reject C, and choose another door: If we get B, we choose B, since B is a better match than C.

If we get A, we choose A, since A is a better match than C. In summary, we win if we see B first, or if we see C and then A. We have increased our chances of getting the best match from 1 in 3, to 1 in 2.

Discussion I adapted the puzzle from a well-known mathematical problem, the Marriage problem, in which the set-up is similar: The context makes many sexist assumptions, of course. The problem is also known as the Secretary problem, in which a boss sees n different candidates for the position of secretary. The calculation is too involved for publication here, but if you are interested there are many web pages on it. Start with the Wiki page , for example.

The answer, however, is simple to state. As a rule of thumb this strategy is often helpful in many situations, not just dating. Reader daze mentioned below the line this morning that they use it to decide which pub to stop in: Please discuss any other applications below!

I set a puzzle here every two weeks on a Monday.


THE DATING GAME was and still is by all accounts, the premiere game show for singles. It was the forerunner for many imitators such as "Love Connection", MTV's "Singled Out" and numerous others. The Dating Game (also known as The New Dating Game and The All-New Dating Game) is the long-running dating game show where one girl or one guy had to choose between three bachelors or bachelorettes to go out on a date for which the producers pay. Generally the bachelorette would ask a series of.

Total 2 comments.
#1 01.08.2018 в 12:10 Playtend0:
Pisaka be killed

#2 03.08.2018 в 19:04 Burebista:
I'm sure, a deep note